This chapter introduces a novel approach for measuring divergent thinking—an acknowledged indicator of creative potential—in higher arts education. The technique is designed to be employed during creative educational tasks and relies on analyzing the semantics of each turn in a dialogue with an LLM-based chatbot through embeddings and cosine distances, thereby capturing the students’ 'semantic leaps' that reveal how the conversation’s conceptual space expands over time. We illustrate this approach in a longitudinal case study. Nine students explored themes from Shakespeare’s Hamlet to create derivative artworks while engaging in turn-by-turn conversations with an AI chatbot. The results of the analysis of the conversations suggest that embedding-based distance metrics can feasibly track creative exploration within higher arts education settings. Moreover, these findings remain consistent across two different language models, suggesting that the technique could be robust to variations in how textual data are encoded. By collecting these quantitative measures in real-time, educators and AI systems could adapt instructional strategies, offering the potential for AI tools to support creativity in arts education.